Relative-Hyper GAGA Theorem

TL;DR

This paper extends Serre's GAGA theorem to a relative hypercohomology setting, establishing an isomorphism between algebraic and analytic relative hypercohomology for complex projective varieties.

Contribution

It introduces a relative hypercohomology version of Serre's GAGA theorem, broadening its applicability to complexes of sheaves and subvarieties.

Findings

Proves isomorphism of relative hypercohomology between algebraic and analytic settings.

Generalizes Serre's GAGA theorem to complexes of sheaves.

Implicates classical GAGA as a special case.

Abstract

In this paper, we provide a relative hypercohomology version of Serre's GAGA theorem. We prove that the relative hypercohomology of a complex of sheaves on a complex projective variety is isomorphic to the relative hypercohomology of its analytification, with respect to an open or closed subvariety. This result implies Serre's original GAGA theorem.